Question

Rewrite the rational expression

Answer 1

Answer:

D. $(x^2+x-1)+\frac{-6}{x+4}$

Step-by-step explanation:

The given rational expression is

$\frac{x^3+5x^2+3x-10}{x+4}$

We obtain the quotient and remainder using synthetic division.

     1     5    3    -10

-4|       -4   -4    4

      1     1     -1    -6

The quotient is $x^3+x-1$ and the remainder is -6.

The expression becomes;

$\frac{x^3+5x^2+3x-10}{x+4}=(x^2+x-1)+\frac{-6}{x+4}$

Answer 2

Answer:

The answer is (D) ⇒ ($x^{2}+x-1)+\frac{-6}{x+4}$

Step-by-step explanation:

∵ $\frac{x^{3}+5x^{2}+3x-10}{x+4}=x^{2}+\frac{x^{2}+3x-10 }{x+4}$

∵ $\frac{x^{2}+3x-10 }{x+4}=x+\frac{-x-10}{x+4}$

∵ $\frac{-x-10}{x+4}=-1+\frac{-6}{x+4}$

∴ The answer is (x² + x - 1) + (-6)/(x + 4)